SOLUTION: Word Problem of Pythagoras' Theorem; Question: PQRS is a rectangle in which PQ = 9 cm and PS = 6 cm. T is a point on PQ such that PT = 7 cm and RV is the perpendicular from R to

Algebra ->  Test -> SOLUTION: Word Problem of Pythagoras' Theorem; Question: PQRS is a rectangle in which PQ = 9 cm and PS = 6 cm. T is a point on PQ such that PT = 7 cm and RV is the perpendicular from R to      Log On


   

Question 954683: Word Problem of Pythagoras' Theorem;
Question: PQRS is a rectangle in which PQ = 9 cm and PS = 6 cm. T is a point on PQ such that PT = 7 cm and RV is the perpendicular from R to ST. Calculate ST and RV.

Please solve this, it's gonna come in exam and it carries 10 marks itself. I tried so hard to solve it but I couldn't. I'd really appreciate it if you guys could solve this! Thanks a lot.
Regards,
Saad Ali
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

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You know that,
PT%5E2%2BPS%5E2=ST%5E2
7%5E2%2B6%5E2=ST%5E2
ST%5E2=49%2B36
ST%5E2=85
ST=sqrt%2885%29
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Find the line that goes through points T and S.
m=%280-6%29%2F%287-0%29=-6%2F7
y-0=-%286%2F7%29%28x-7%29
y%5BST%5D=-%286%2F7%29x%2B6
The perpendicular line would have a slope that is the negative reciprocal,
m%5Bp%5D=7%2F6
So the perpendicular line through R would be,
y-6=%287%2F6%29%28x-9%29
y-6=%287%2F6%29x-21%2F2
y=%287%2F6%29x-21%2F2%2B12%2F2
y%5Bperp%5D=%287%2F6%29x-9%2F2
Find the point of intersection (V) using these two lines,
-%286%2F7%29x%2B6=%287%2F6%29x-9%2F2
-%286%2F7%2B7%2F6%29x=-9%2F2-12%2F2
-%2885%2F42%29x=-21%2F2
x=441%2F85
Then,
y=1029%2F170-765%2F170
y=264%2F170
y=132%2F85
Now that you have V use the distance formula,
D%5BRV%5D%5E2=%289-441%2F85%29%5E2%2B%286-132%2F85%29%5E2
D%5BRV%5D%5E2=%28324%2F85%29%5E2%2B%28378%2F85%29%5E2
D%5BRV%5D%5E2=%28104976%2B142884%29%2F%2885%29%5E2
D%5BRV%5D%5E2=%28247860%29%2F%2885%29%5E2
D%5BRV%5D%5E2=%282916%29%2F%2885%29
D%5BRV%5D=sqrt%282916%2F85%29
D%5BRV%5D=%2854%2F85%29sqrt%2885%29